Turn Left

Taro got a driver's license with great effort during his campus days, but unfortunately he had no opportunities to drive. He ended up obtaining a gold license.

One day, he and his friends made a plan to go on a trip to Kyoto with you. At the end of their meeting, they agreed to go around by car, but there was a big problem: none of his friends was able to drive a car. Thus he had no choice but to become the driver.

The day of departure has come. He is going to drive but would never turn to the right for fear of crossing an opposite lane (note that cars keep left in Japan). Furthermore, he cannot U-turn for lack of technique. The car is equipped with a car navigation system, but the system cannot search for a route without right turns. So he asked you: "I hate right turns, so could you write a program to find the shortest left-turn-only route to the destination, using the road map taken from this navigation system?"

The input consists of multiple data sets. The first line of the input contains the number of data sets. Each data set is described in the format below:

m n
name1 x1 y1
...
namem xm ym
p1 q1
...
pn qn
src dst

m is the number of intersections. n is the number of roads. namei is the name of the i-th intersection. (xi, yi) are the integer coordinates of the i-th intersection, where the positive x goes to the east, and the positive y goes to the north. pj and qj are the intersection names that represent the endpoints of the j-th road. All roads are bidirectional and either vertical or horizontal. src and dst are the names of the source and destination intersections, respectively.

You may assume all of the following:

• 2 ≤ m ≤ 1000, 0 ≤ xi ≤ 10000, and 0 ≤ yi ≤ 10000;
• each intersection name is a sequence of one or more alphabetical characters at most 25 characters long;
• no intersections share the same coordinates;
• no pair of roads have common points other than their endpoints;
• no road has intersections in the middle;
• no pair of intersections has more than one road;
• Taro can start the car in any direction; and
• the source and destination intersections are different.

Note that there may be a case where an intersection is connected to fewer than three roads in the input data; the road map may not include smaller roads which are not appropriate for non-local people. In such a case, you still have to consider them as intersections when you go through them.

For each data set, print how many times at least Taro needs to pass intersections when he drives the route of the shortest distance without right turns. The source and destination intersections must be considered as "passed" (thus should be counted) when Taro starts from the source or arrives at the destination. Also note that there may be more than one shortest route possible.

Print "impossible" if there is no route to the destination without right turns.